Jonathan,
JONATHAN:
As Glenn points out I was careless about using the word "absolute" rather
than "complete" in referring to Goedel's theorem. However, I do not believe that
it changes the essence of my argument.
I believe it does if your argument has anything to do with Godel's thm.
> JONATHAN:
> In an earlier post, reference was made to Goedels theorem, which states
> that an infinite number of axioms are needed to make a system absolute.
>
GLENN:
>No, this is not what Godel's theorem states.
JONATHAN:
Had I written "complete", Glenn would probably have accepted the
definition.
Pretty much.
JONATHAN:
Goedel's "incompleteness" theorem states that no statement
can be proved without reference to an external fact or axiom.
No, this is not what Godel's theorem states. This is what any formal
system demands.
JONATHAN:
Once you internalize the "external" axiom, still more external axioms are
needed. Thus no statement can ever be "absolutely" complete.
No, it's not that no statement can ever be "absolutely" complete. It's that
no system can be absolutely complete. The theorems (statements) in the
system are fine.
JONATHAN:
If it always depends on reference to external axioms, it must also be
RELATIVE to the external axioms chosen (i.e. non absolute).
All theorems are directly or indirectly proved from the axioms, but
this is true of any formal system and has nothing to do with the
conclusions of Godel's Thm.
Glenn
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